1. Field of the Invention
The present invention relates to an apparatus for automatically generating a constraint condition of a molecule in a molecular dynamics method. The apparatus can be used in a device for simulating the behavior of a molecule using a computer, based on the molecular dynamics method, for the purpose of developing a new substance, for example.
2. Description of the Related Art
An application technology for a super-computer, for example, which is suitable for high-speed scientific and engineering computation, is a simulator utilizing the molecular dynamics method. The simulator receives the initial coordinates of an atom, the initial speed of an atom, a potential function between atoms, the mass of an atom, and the electric charge of an atom, for example, and simulates the behavior of a molecule based on the molecular dynamics method, thereby obtaining the properties of a substance.
A constraint condition for freezing or limiting some parts of the degrees of freedom within the molecule is provided as input information for the simulator. The molecular dynamics method is used in order to examine the effect of a predetermined force applied between the atoms when a simulation is performed by using the molecular dynamics method. In this case, technology for generating the constraint condition with accuracy and ease is required.
Before explaining the prior art of the apparatus for generating the constraint condition using the molecular dynamics method, a summary of the molecular dynamics method will be briefly given. The molecular dynamics method performs a computer simulation of a behavior of molecules by moving the particles using the laws of motion according to classical dynamics to examine a property of a multiparticle system composed of many particles. This method itself is relatively old but many improvements of this method have been proposed since 1980. Thus, the range of subjects capable of being studied by using the molecular dynamics method has been greatly expanded. This is because a method for performing a simulation under the conditions of constant temperature and pressure has been developed, although the phenomena were conventionally examined under the conditions of constant energy and volume.
In the field of computational physics, which concerns the development of new substances or materials, a method for non-empirically calculating molecular orbits is now practically used for development of small-molecule materials with small numbers of electrons. The cooperation of calculation, synthesis and substance property measurement is becoming a new style of a molecular development. On the other hand, for material design with multi-particles bodies of atoms and molecules comprising several hundreds to several thousands of atoms or several ten thousands of atoms depending on the subject, application of electronic theory is still difficult at present even though the capacity of computers approaches the order of GFLOPS. Classical molecular dynamics using a potential function between atoms or between molecules is, therefore, still used as the dominant method.
Before a computer simulation is introduced, statistical dynamics is used for examining the structure and properties of a group of many atoms and molecules based on microscopic information such as an interaction force applied between atoms. However, when the interaction force between atoms becomes rather complicated, it becomes impossible to obtain an exact solution of the basic formulas of statistical dynamics. The molecular dynamics method is a simulation method for applying Newton's equations for a multiparticle system in a numerical analysis and providing information similar to that obtained from the statistical dynamics method.
FIG. 1 (PRIOR ART) shows input information and output information according to the molecular dynamics method. As the input information, a potential function representing an interaction force applying between atoms or molecules and physical environmental conditions such as temperature and pressure are supplied. Newton's equations for multiparticle systems are solved under the potential function. Also, physical environmental conditions and the positional coordinates of an atom at successive points in time, which are obtained as the solution of the Newton equations, are subjected to statistical processing. Thermodynamics properties such as internal energy, and the elastic constant are provided as the output information. Further, the positional coordinates and velocities of the atoms at successive points in time are subjected to statistical processing, thereby providing dynamic properties such as the diffusion coefficient, viscosity coefficient, electrical conductivity and thermal conductivity, and spectroscopic properties as the output information.
The molecular dynamics simulation method uses as its subject a substance comprising a large number of molecules such as liquid and produces a motion of representative molecules by using a computer simulation, thereby providing macroscopic properties of the substance. By using a method of performing a simulation under conditions of constant temperature and pressure, it becomes possible to directly examine the arrangement of particles within a crystal and a structural phase transfer in which the form of the crystal changes. Naturally, the number of particles and the time used for the analysis is greatly limited by the computation calculation capability of the computer. The problem of the simulation is how to study a macroscopic property by using a small particle system in an efficient manner.
Next, the prior art relating to the constraint condition which is the subject of the present invention will be explained. FIG. 2 (PRIOR ART) shows an explanatory view of a bond, angle and torsion to explain the technical background of the present invention. FIGS. 3 and 4 are for explaining views of the constraint condition, FIGS. 5 and 6 show explanatory views of a predetermined constraint condition and FIGS. 7 and 8 are for explaining the potential function. When a constraint condition comprising a list of a constrained atom and a bond, angle and torsion of the constrained atom is generated to perform a simulation of the behavior of a molecule based on the molecular dynamics method by using a computer, conventionally, a user manually inputs the number of the atom and numerical values of bonds, angles and torsions in an input frame displayed on a display screen.
A bond constraining an atom is a bonding distance of two atoms I and J as shown in FIG. 2A. An angle is a bonding angle&lt;IJK of three atoms I, J, K as shown in FIG. 2B. A torsion is an angle .phi. between a plane formed by three atoms, I, J, K and a plane formed by three atoms, I, L and K with two atoms I and K common to both planes with regard to four atoms I, J, K and L as shown in FIG. 2C.
Where the degrees of the freedom of the acetic acid molecule (CH.sub.3 COOH) with a chemical structure formula as shown in FIG. 3A are constrained to some extent, it is necessary to form a bond constraint list as shown in FIG. 3B, an angle constraint list as shown in FIG. 4A and a torsion constraint list as shown in FIG. 4B. The numbers 1 through 8 are attached to respective atoms in FIG. 3A for sequential numbering of the atoms within the molecule.
The contents of the bond constraint list shown in FIG. 3B represent that a distance between two atoms is constrained to a value provided as a bonding distance and 1 4 1.4 , for example, represent that the inter-atom bonding distance between H with the number 1 and C with the number 4 is constrained to be 1.4A. The contents of the angle constraint list shown in FIG. 4A represent that the angle is constrained to a value and 1 4 2 109.4 , for example, represents that the central angle 1-4-2 formed by H with the number 1, H with the number 2 and C with the number 4 is constrained to be 109.4.degree. degrees.
Further the contents of the torsion constraint list shown in FIG. 4B represent that the torsion is constrained to the given value, and 4 5 7 8 180 , for example, represents that an angle .phi. between a plane 4-5-7 (namely, the plane formed by atoms 5, 4 and 7) and a plane 5-7-8 (namely, the plane formed by atoms 5, 8, and 7) is constrained to be 180.degree. degrees.
A partial constraint may be applied, for example, only a torsion (4-5-7-8) of acetic acid shown in FIG. 5A is constrained, such that the torsion between plane 4-5-7 and plane 5-7-8 is constrained to be 180.degree. degrees, for example. Then a bond constraint list, angle constraint list, and torsion constraint list as shown in FIGS. 5B to 5D are required. This is because when the torsion is constrained, the angle and bond forming the torsion should also be constrained.
Likewise, when only the angle (5-7-8) of acetic acid on FIG. 6A is constrained to be 109.4.degree. degrees for example, the bond constraint list shown in FIG. 6B and the angle constraint list shown in FIG. 6C are required. This is because where the angle is constrained, all the bonds forming the angle should be constrained. The bond constraint list for constraining only the bond (5-7) is shown in FIG. 6D. As described above it should be noted in a given partial constraint that where the torsion is constrained, all the angles and the bonds forming the torsion should be constrained and where the angle is constrained, all the bonds forming the angle should be constrained. If these two conditions are not satisfied, a contradiction arises.
A bond potential function, angle potential function, or torsion potential function should be provided for a bond, angle or torsion to which a constraint is not applied the behavior of the molecule being simulated by using these potential functions. For example, a harmonic-type bond potential function is as shown in FIG. 7A and a harmonic-type angle potential function is as shown in FIG. 7C. A harmonic-type torsion potential function is as shown in FIG. 8A. When the bond potential function E(l) is partially differentiated with respect to variable (l), the force acting between atoms I and J in FIG. 2A is obtained. When the angle potential function E(.theta.) is partially differentiated with respect to variable .theta., the force acting between atoms I and K in FIG. 2B is obtained. When the torsion potential function E (.phi.) is partially differentiated with respect to variable .phi., the force acting between atoms J and L in FIG. 2C is obtained.
When none of the bonds of the acetic acid molecule are constrained, the bond potential parameters as shown in FIG. 7B are required. Likewise, when none of the angles of the acetic acid molecule are constrained, the angle potential parameters as shown in 7D are required. When none of the torsions of the acetic acid molecule are constrained, under the condition that the bonds and angles are not constrained, the torsion potential parameters as shown in FIG. 8B are required.
When a simulation is performed based on the molecular dynamics method under a constraint condition in which some of the degrees of internal freedom within the molecule are frozen, conventionally a user has to prepare a constraint list as shown in FIGS. 3 and 4 manually and in advance, and input it into a simulator for use in the molecular dynamics method. Accordingly, the work efficiency is extremely low and thus the conventional manual method is not suitable for macromolecules having many atoms in a molecule.
When the torsion is constrained, all the angles and the bonds forming the torsion should be constrained. When the angle is constrained, all the bonds forming the angle should be constrained. However, these requirements are not always followed due to input of insufficient constraint conditions, thereby causing a contradiction and making the computation difficult.
Further, a potential function should be assigned to a torsion to which a constraint is not applied, as shown in FIGS. 7 and 8. But this is extremely troublesome and time consuming for an operator to perform such assignment manually.